The
y
-coordinate of each point on the graph of
y = (f + g)(x)
is the result
of adding the
y
-coordinate of
g(x)
to the
y
-coordinate of
f (x)
. For
example, as noted above,
f (1) = 3
,
g(1) = 3
, and
(f + g)(1) = 3 + 3 = 6
.

The slope of
f
is 2; in other words, as
x
increases
by 1,
f (x)
increases by 2. The slope of
g
is 1: as
x
increases by 1,
g(x)
increases by 1. Thus, as
x
increases by 1,
f + g
increases by 2 + 1
= 3, and the slope of the sum of two linear functions is the sum of their
slopes. The
y
-intercept of
f + g
is also a combination of the
y
-
intercepts of
f
and
g
: -1 + 4 = 3.

Adding two functions is like plotting one function and taking the graph of that
function as the new
x
-axis. Points of the second function are then plotted
with respect to the new axis. For example, (2, 3) becomes "over 2," "up 3 from
the new axis," or
(3, f + 2)
.

The
y
-coordinate of each point on the graph of
y = (f - g)(x)
is the result
of subtracting the
y
-coordinate of
g(x)
from the
y
-coordinate of
f (x)
.
For example, as noted above,
f (2) = 3
,
g(2) = 6
, and
(f - g)(2) = 3 - 6 = - 3
.